There is proposed a vehicle having accelerating/decelerating means for running the vehicle in an alternately accelerating and decelerating mode by alternately repeating an accelerating run and a decelerating run of the vehicle at a running speed varying between upper and lower limits which are set on the basis of a predetermined target running speed of the vehicle. Patent Document 1 discloses an example of such a vehicle, which is run in the alternately accelerating and decelerating mode described above so as to improve the fuel economy of the vehicle, in an automatic cruising control mode in which a vehicle drive power source is automatically controlled to run the vehicle at the target running speed set by an operator of the vehicle. Namely, where the vehicle is run in the automatic cruising control mode at relatively low running speeds at which an engine is required to be operated in an operating region of a comparatively low operating efficiency, the vehicle is run in the alternately accelerating and decelerating mode described above such that the accelerating run is performed with the engine operated in an operating region of a high operating efficiency, while the decelerating run is performed in a gliding mode with a small running resistance with the engine held at rest, so that the overall fuel economy of the vehicle can be improved.